Smarandache curves for spherical indicatrix of the Bertrand curves pair

Şenyurt, Süleyman; Altun, Yasin; Cevahir, Ceyda

doi:10.5269/bspm.v38i2.33899

Cited by 4 publications

(3 citation statements)

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“…respectively. More information about Smarandache curves can be found in [1], [3], [25], [27] and etc. On the other hand, the coefficients of the first and the second fundamental forms of a local parametrization of a spacelike or timelike surface…”

Section: Introductionmentioning

confidence: 99%

Ruled and Rotational Surfaces Generated by Non-Null Curves with Zero Weighted Curvature in $(\mathbb{L}^{3},ax^{2}+by^{2})$

Altin

Kazan

Karadağ

2020

International Electronic Journal of Geometry

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In this study, firstly we give the weighted curvatures of non-null planar curves in Lorentz-Minkowski space with density e ax 2 +by 2 and obtain the planar curves whose weighted curvatures vanish in this space under the condition that the constants a and b are not zero at the same time. After giving the Frenet vectors of the non-null planar curves with zero weighted curvature in Lorentz-Minkowski space with density e ax 2 , we create the Smarandache curves of them. With the aid of these curves and their Smarandache curves, we get the ruled surfaces whose base curves are non-null curves of which vanishing weighted curvature and ruling curves are Smarandache curves of them. Followingly, we give some characterizations for these ruled surfaces by obtaining the mean and Gaussian curvatures, distribution parameters and striction curves of them. Also, rotational surfaces which are generated by non-null planar curves with zero weighted curvatures in Lorentz-Minkowski space E 3 1 with density e ax 2 +by 2 are studied under the condition that the constants a and b are not zero at the same time. We draw the graphics of the obtained surfaces.

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Section: Introductionmentioning

confidence: 99%

Ruled and Rotational Surfaces Generated by Non-Null Curves with Zero Weighted Curvature in $(\mathbb{L}^{3},ax^{2}+by^{2})$

Altin

Kazan

Karadağ

2020

International Electronic Journal of Geometry

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“…Since the Smarandache curves play an important role in Smarandache geometry, many geometers have been interested in these curves. More information about Smarandache curves can be found in [1], [2], [18], [19].…”

Section: Introductionmentioning

confidence: 99%

Rotational Surfaces Generated by Planar Curves in E3 with Density

Altin

Kazan

Karadağ³

2019

ijaa

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“…Turgut ve Yılmaz, Minkowski uzay-zamanda konum vektörü başka bir eğrinin Frenet vektörleri tarafından oluşturulan yeni eğriyi Smarandache eğrisi olarak adlandırmışlardır [14]. Daha sonra bu eğriler farklı uzaylarda farklı çatılar ele alınarak incelenmiş ve yeni sonuçlar elde edilmiştir.…”

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3-Boyutlu Minkowski Uzayında İnvolüt-Evolüt Eğrilerinin TB ve NB -Smarandache Eğrileri

Kalkan

Zeybek²

2019

Bitlis Eren Üniversitesi Fen Bilimleri Dergisi

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Smarandache curves for spherical indicatrix of the Bertrand curves pair

Abstract: In this paper, we investigate special Smarandache curves with regard to Sabban frame for Bertrand partner curve spherical indicatrix. Some results have been obtained. These results were expressed depending on the Bertrand curve. Besides, we are given examples of our results.

Cited by 4 publications

References 4 publications

Ruled and Rotational Surfaces Generated by Non-Null Curves with Zero Weighted Curvature in $(\mathbb{L}^{3},ax^{2}+by^{2})$

Ruled and Rotational Surfaces Generated by Non-Null Curves with Zero Weighted Curvature in $(\mathbb{L}^{3},ax^{2}+by^{2})$

Rotational Surfaces Generated by Planar Curves in E3 with Density

3-Boyutlu Minkowski Uzayında İnvolüt-Evolüt Eğrilerinin TB ve NB -Smarandache Eğrileri

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Smarandache curves for spherical indicatrix of the Bertrand curves pair

Abstract: In this paper, we investigate special Smarandache curves with regard to Sabban frame for Bertrand partner curve spherical indicatrix. Some results have been obtained. These results were expressed depending on the Bertrand curve. Besides, we are given examples of our results.

Cited by 4 publications

References 4 publications

Ruled and Rotational Surfaces Generated by Non-Null Curves with Zero Weighted Curvature in $(\mathbb{L}^{3},ax^{2}+by^{2})$

Ruled and Rotational Surfaces Generated by Non-Null Curves with Zero Weighted Curvature in $(\mathbb{L}^{3},ax^{2}+by^{2})$

Rotational Surfaces Generated by Planar Curves in E3 with Density

3-Boyutlu Minkowski Uzayında İnvolüt-Evolüt Eğrilerinin T*B* ve N*B* -Smarandache Eğrileri

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3-Boyutlu Minkowski Uzayında İnvolüt-Evolüt Eğrilerinin TB ve NB -Smarandache Eğrileri